3D Model for Active Vibration Control of Rotating Machines Mounted on Active Machine Foot Mounts Using Vibration Mode Coupling by Asymmetry

Abstract

Purpose In this work, active vibration control of rotating machines mounted on active machine foot mounts is investigated. Methods Therefore, a simplified 3D model is derived and the mathematical coherences are described. Different mathematical solutions are presented for special boundary conditions and a method called “vibration mode coupling by asymmetry” is derived. Results It could be shown that a symmetrical system with a machine design, where the center of gravity lies symmetrically between the machine feet with a vertical distance, and where all actuators are identical, represents a system, where all vibration shapes but one can be influenced by the controllers, when the gyroscopic effect can be neglected. In this case, a special vibration shape occurs—where the machine is only rotating at its vertical axis—which cannot be influenced by the controllers. When the stiffness and/or damping in axial and/or horizontal direction of only one actuator will be changed—which will lead to an asymmetrical system—the vibration shape with pure rotation at the vertical axis will not exist anymore. Now, the vibration shapes will become more coupled and they all can be influenced by the controllers, which is here called “vibration mode coupling by asymmetry”. Conclusions With the here presented method of “vibration mode coupling by asymmetry”, all vibrations mode shapes can now be active controlled.

A Complex Vibration Analysis of a Drive System Equipped with an Innovative Prototype of a Flexible Torsion Clutch as an Element of Pre-Implementation Testing

“…The results obtained are comparable with the results obtained during our research. The amplitude response functions for the bearing housing vibration velocity depending on the rotor speed for a symmetrical and asymmetrical system and many more numerical experiments are presented in [ 49 ]. The research object was a model of rotating machines mounted on active machine foot mounts using vibration mode coupling by asymmetry.…”

Generalized mathematical formulation for active vibration control of rotating machines with voltage‐driven electrodynamic actuators between machine feet and steel frame foundation

“…In [27][28][29] mathematical descriptions have been developed for vibration control of special vibration models for rotating machines, where actuators as basic elements between machine feet and steel frame foundation have been used. It could be shown that all critical mode shapes can be actively damped, although only vertical forces are produced by the actuators, using the idea of vibration mode coupling by asymmetry, based on [28]. One enhancement of the here presented papercompared to [27][28][29]-is now, that not only actuators as basic elements are used but specific actuators-voltage-driven electrodynamic actuators-and also their typical transfer functions.…”

“…One enhancement of the here presented papercompared to [27][28][29]-is now, that not only actuators as basic elements are used but specific actuators-voltage-driven electrodynamic actuators-and also their typical transfer functions. Another important modification over [27][28][29] is, that here in this paper now the state space vector is used for controller feedback instead of the output vector, which leads in combination with the voltage-driven electrodynamic actuators and their inherent system character to less complex mathematical formulations. This leads to the next modification that two separate feedback loops are used here for calculating the actuator forces in the state-space formulation instead of only one feedback loop in [27][28][29].…”

“…Another important modification over [27][28][29] is, that here in this paper now the state space vector is used for controller feedback instead of the output vector, which leads in combination with the voltage-driven electrodynamic actuators and their inherent system character to less complex mathematical formulations. This leads to the next modification that two separate feedback loops are used here for calculating the actuator forces in the state-space formulation instead of only one feedback loop in [27][28][29]. One feedback loop is used here to calculate the actuator forces, which only depend on the relative velocities between armatures and stators of the actuators, and one feedback loop for the actuator forces, which only depend on the supply voltages of the controllers (see Section 2.2).…”

“…An additional important enhancement-compared to [27][28][29]-is, that in this paper a generalized mathematical formulation is developed for active vibration control of any kind of rotating machine with voltage-driven electrodynamic actuators between machine feet and an elastic foundation (e.g., steel frame foundation), which can be used, independent of the level of detail of the model, for example, 1D-, 2D-, and 3D-models, whereas in [27][28][29] the mathematical formulations represent always a special model. The advantage of the here presented closed mathematical formulation compared to, for example, mathematical formulations for block diagram-based simulation tools is, that for a harmonic analysis by excitation with rotor angular frequency, for example, due to mechanical unbalance-which is typical for rotating machines-frequency dependent matrices like the stiffness and damping matrix (if e.g.…”